Neurotwins (tES 2.0): Advancing Brain Simulation

Introduction

Welcome back to our exploration of neurotwins. In the first part, we explored the creation of Neurotwins through biophysical head models, using advanced imaging techniques like MRI and image segmentation algorithms to develop detailed 3D brain models. These models enabled precise simulations of electrical currents for personalized neuromodulation therapy.

In this second part, we will discuss Neurotwins (tES 2.0), which build upon these biophysical head models to include advanced simulations. These simulations focus on neuronal reactions to electric fields and interneuronal connectivity and interactions, offering a deeper understanding of brain dynamics.

Despite their utility, biophysical head models offer only a partial representation of the brain. The most notable limitation is their composition: devoid of interacting neurons and firing spikes, they consist of non-responsive tissue. While these models accurately predict the propagation of currents through various layers and the distribution of neurons, particularly within gray matter, they lack insights into neuronal reactions to electric fields and interneuronal connectivity and interactions.

Picture this!

To illustrate this limitation, consider the previous city analogy, where different areas like urban, countryside, and water bodies have been delineated or “segmented”. While we can infer tendencies, such as people congregating in urban or countryside areas, the model falls short in predicting interactions or responses to external stimuli, like an earthquake.

Addressing this gap is the physiology model, which, in conjunction with the biophysical head model, constitutes a Neurotwin.

Physiology model

Understanding the available data

Constructing the physiology model, also referred to as the brain network model, necessitates a comprehensive understanding of available brain data. To achieve personalization, we can incorporate diverse data modalities. Our main focus, currently, is functional data, particularly Electroencephalography (EEG) and functional Magnetic Resonance Imaging (fMRI).

Key point: What is EEG?

EEG is a valuable technique used to measure the electrical activity of the brain. By placing electrodes along the scalp, EEG records the spontaneous electrical signals generated by the brain’s neurons. These signals, known as biosignals, offer insights into the functioning of the brain, revealing patterns of activity associated with various cognitive processes and states. EEG is non-invasive and widely used in clinical and research settings due to its ability to provide real-time data on brain activity [8].

Neuroelectrics offers its own wireless solution for EEG called Enobio. You can check it out here.

Imagine a city…

To illustrate this limitation, consider the previous city analogy, where different areas like urban, countryside, and water bodies have been delineated or “segmented”. While we can infer tendencies, such as people congregating in urban or countryside areas, the model falls short in predicting interactions or responses to external stimuli, like an earthquake.

But here’s the catch!

While EEG gives us quick insights into what’s happening in the brain right now, it would be similar to listening to Atlantis from the boat we had before. Sure, with some powerful microphones, you would be able to catch some sound but you might have difficulties pinpointing from which street or house it’s coming. In short, EEG is useful for recording general brain activity and has a high temporal resolution, but at the expense of a low spatial one.

Fig 7: Left: Human EEG with prominent resting state activity, taken from Wikipedia [8]. Right: Speech waveform, taken from [9].

Key concepts: fMRI

Functional MRI (fMRI)

Functional Magnetic Resonance Imaging (fMRI) is a sophisticated neuroimaging technique utilized to observe brain activity by measuring changes in blood flow. By detecting alterations in blood oxygenation levels, fMRI can map the regions of the brain that are active during different tasks or in various states. In short, fMRI indirectly measures the activity of the brain areas by looking at the changes in blood flow — more flow means more activity.

Unlike traditional MRI, which provides static images of brain structure, fMRI offers dynamic insights into brain function. It is a non-invasive method that allows researchers and clinicians to investigate neural processes associated with cognition, perception, emotion, and behavior. fMRI has revolutionized neuroscience research and clinical diagnostics by enabling the visualization of brain activity in unprecedented detail. Its widespread application has significantly advanced our understanding of the human brain and its complexities.

Back to our city… and how it related to fMRI

Now, consider your trusted navigation app or the traffic maps shown in TV, which are all based on tracking traffic flow using data from millions of drivers’ GPS devices or road cameras. They provide eyes all over the road, giving us almost real-time updates on congestion, accidents, and detours. This service offers highly detailed information on which roads are jammed or have accidents, thanks to its high spatial resolution. However, its temporal resolution is a bit slower, as it averages data from several minutes rather than providing instantaneous updates.

Similarly, fMRI offers an excellent spatial resolution on brain activity, but at the expense of a lower temporal resolution, usually on the order of seconds.

Fig 8. Left: Transit activity in Barcelona during 8 am, captured from [10]. Right: Blood-oxygen-level-dependent (BOLD) signal changes experienced during tACS stimulation, adapted from [11].

Building a whole brain model

A whole brain model comprises a network of mathematical entities that simulate neurons or neural populations. On one side, we need to establish how the network is connected which, again, is informed by personalized real data. Specifically, the connections among brain areas are given by the connectome, a graph representation of the wiring of the human brain which can be estimated using non-invasive diffusion MRI. On the other side, we need a model for neurons or large populations and how they interact with the electric fields generated by tES.

Key concepts: Neuroal Mass Models

Neuroal Mass Models (NMM)

A whole brain model consists of a network of mathematical entities that simulate neurons or neural populations. In our case, we simulate neural populations using a mathematical model called Neural Mass Model, which uses stochastic second-order differential equations to describe the behavior of large populations of neurons in the brain as a single entity [12-14]. Or, in simpler terms, we have tools to simulate their average, but not exact, behavior over time, since the model considers that there is a stochastic or random component to it.

On top of it, these models are able to incorporate how the populations respond to stimuli, that is, to an external perturbation due to tES or due to the interaction with other brain regions. 

You can read more about it in The emergence of second-generation neural mass models post.

A bigger picture: modeling a whole region!

Back to the city example, it may be useful now to zoom out and consider the whole Catalan region as an analogy for the whole brain. We could try to model each individual person. Not only would it take an unreasonable amount of resources, but also add a lot of uncertainty in our model. Instead, we could focus on regions and cities as the main entities.

Fig 9. Topographic map of Catalunya, scale 1:1.000.000. Institut Cartogràfic i Geològic de Catalunya [15]. Annotated image of five cortical columns showing the 6 layers of the cortical and the pial surface and the white matter. Taken from Wikipedia [16] and ultimately adapted from [17].

Simulating the behavior of each individual person would mean simulating the behavior of over 8 million people. Even if the behavior of each person and how they interact with the world could be simulated with a single equation – which typical models are more complex – that would mean solving more than 8 million equations. For the brain, which has approximately 100 billion neurons, it would take an unfeasible amount of computational power.

Instead, we could split Catalunya into several regions and model each one as an entity. For instance, it could be divided into comarques, which are 43 areas centered around one or two main towns. In a similar way, we can parcellate – divide into parcels or areas – the brain.

Fig 10. Catalan comarques. Institut Cartogràfic i Geològic de Catalunya [18].

We could then compare the modeling of what in a smaller region – like a comarca – to a neural mass model and, thus, consider that each city and town is what we referred to as neural populations. The only problem? There are more than 900 towns and thousands of small roads and trails connect them! We could still simplify more and take only the main cities and main roads and group other relevant urban areas and paths.  Similarly, when defining the elements of a neural mass model, we focus only on the largest populations and those most relevant to the pathology we want to treat.

Fig 11. Left: The Vallès Occidental comarca, with the main roads highlighted and the main cities shaded in blue, green, and orange. Adapted from Google Maps [19]. Right: Laminar Neural mass model diagram, representing two pyramidal populations and three interneuron populations. Adapted from [20].

For building whole brain models, we usually consider that all neural mass models have the same architecture, that is, the populations studied are the same, although their behavior can change. The strength of the connections between populations can also be modified. It would be similar to considering that we divided Catalunya into regions and each one has always 5 main urban areas connected, although the size of the roads or how people live in each urban area can vary.

Personalizing and optimizing a Neurotwin

Combining both the physiology model and the biophysical head model yields a prototype of a Neurotwin, capable of simulating not only the behavior of neural populations but also biophysical signals such as EEG or fMRI. To accomplish this, we utilize additional models that leverage the neural activity generated by the neural mass models.

Modifying the model parameters—dictating the behavior of each neural population and their interconnections—allows us to alter the simulated signals. Yet again, we encounter an optimization challenge: finding the optimal parameters to match patient data. With thousands of potential parameter combinations, finding the best solution seems nearly impossible without the aid of clever algorithms

Conclusion

While genetic algorithms and their variants, such as differential algorithms, remain viable options, we at Neuroelectrics are actively advancing our research to develop more effective parameter fitting and optimization algorithms. This includes exploring techniques borrowed from deep learning algorithms, a promising avenue for further improvement.

Similarly, once a Neurotwin is personalized, we can simulate the effects of the electric field given a montage and optimize for a desired effect. We will delve deeper into this topic in a more advanced post. Stay tuned!

References:

[8] Electroencephalography article at Wikipedia: https://en.wikipedia.org/wiki/Electroencephalography 

[9] Tom Bäckström et al. Speech processing book. Aalto University. https://speechprocessingbook.aalto.fi/Representations/Waveform.html 

[10] Mapa continu de trànsit (MCT): https://mct.gencat.cat/  

[11] Mencarelli, L., Monti, L., Romanella, S., Neri, F., Koch, G., Salvador, R., … & Santarnecchi, E. (2022). Local and distributed fMRI changes induced by 40 Hz gamma tACS of the bilateral dorsolateral prefrontal cortex: a pilot study. Neural Plasticity, 2022.

[12] Wilson, H. R., & Cowan, J. D. (1972). Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical journal, 12(1), 1-24.

[13] Lopes da Silva, F. H., Hoeks, A., Smits, H., & Zetterberg, L. H. (1974). Model of brain rhythmic activity: the alpha-rhythm of the thalamus. Kybernetik, 15, 27-37.

[14] Jansen, B. H., & Rit, V. G. (1995). Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns. Biological cybernetics, 73(4), 357-366.

[14] Wendling, F., Bartolomei, F., Bellanger, J. J., & Chauvel, P. (2002). Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition. European Journal of Neuroscience, 15(9), 1499-1508.

[15]  Mapa topogràfic 1:1.000.000.  Institut Cartogràfic i Geològic de Catalunya. https://www.icgc.cat/Ciutada/Descarrega/Mapes-topografics/Mapa-topografic-1-1.000.000 

[16] Cortical column article at Wikipedia. https://en.wikipedia.org/wiki/File:Cortical_Columns.jpg 

[17] Oberlaender, M., Narayanan, R., Egger, R., Meyer, H., Baltruschat, L., Dercksen, V., … & Sakmann, B. (2014). Beyond the Cortical Column-Structural Organization Principles in Rat Vibrissal Cortex. In Front. Neuroinform. Conference Abstract: 5th INCF Congress of Neuroinformatics. doi: 10.3389/conf. fninf (Vol. 52).

[18] Maps de comarques mut. Institut Cartogràfic i Geològic de Catalunya. https://www.icgc.cat/L-ICGC/Sobre-l-ICGC/Recursos-didactics/Mapes-de-comarques 

[19] Google maps.https://www.google.com/maps 

[20] Sanchez-Todo, R., Bastos, A. M., Lopez-Sola, E., Mercadal, B., Santarnecchi, E., Miller, E. K., … & Ruffini, G. (2023). A physical neural mass model framework for the analysis of oscillatory generators from laminar electrophysiological recordings. NeuroImage, 270, 119938.

Images:

All images are either referenced, generated in-house or, in the case of the illustrative drawings, generated by Dall·E 3.